Non-fragile distributed state estimation over sensor networks subject to DoS attacks: the almost sure stability

Abstract

This paper focuses on the non-fragile distributed state estimation of discrete-time nonlinear systems over sensor networks subject to DoS attacks, whose probabilistic characterisations are adopted to reflect the reality better. On the basis of considering DoS attacks and gain variations, a non-fragile distributed state estimator is designed by fusing the innovation from the adjacent estimators and itself. In light of a switching idea, an auxiliary function on the product term of attack signals is exploited to disclose the evolution of the Lyapunov function. By virtue of the limit theorem and the developed evolution rule, a sufficient condition is proposed to guarantee that the error dynamics are almost surely asymptotical stable. Furthermore, gain variations are handled by utilising the well-known S-procedure, and the desired estimator gains are designed via a set of solutions of matrix inequalities. Finally, the effectiveness of the developed results is illustrated by a numerical example.

Keywords:

• Distributed state estimation
• sensor networks
• DoS attacks
• almost sure stability

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61973219 and 61933007, the Natural Science Foundation of Shanghai under Grant 18ZR1427000, and the Natural Science Foundation of Universities in Anhui Province under Grants gxyqZD2019053 and KJ2019A0160.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grants number 61973219 and 61933007], the Natural Science Foundation of Shanghai [grant number 18ZR1427000], and the Natural Science Foundation of Universities in Anhui Province [grants number gxyqZD2019053 and KJ2019A0160].

Notes on contributors

Jinhua Song

Jinhua Song received the BSc degree in Mathematics and Applied Mathematics from Qingdao University of Science and Technology, Qingdao, China, in 2018. She is currently pursuing a master’s degree in Operations Research and Cybernetics from University of Shanghai for Science and Technology, Shanghai, China. Her current research interests is Control and filtering of networked systems.

Derui Ding

Derui Ding received the BSc degree in industry engineering and the MSc degree in detection technology and automation equipment from Anhui Polytechnic University, Wuhu, China, in 2004 and 2007, respectively, and the PhD degree in control theory and control engineering from Donghua University, Shanghai, China, in 2014. From July 2007 to December 2014, he was a Teaching Assistant and then a Lecturer with the Department of Mathematics, Anhui Polytechnic University. He is currently a Senior Research Fellow with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC, Australia. From June 2012 to September 2012, he was a Research Assistant with the Department of Mechanical Engineering, University of Hong Kong, Hong Kong. From March 2013 to March 2014, he was a Visiting Scholar with the Department of Information Systems and Computing, Brunel University London, Uxbridge, UK. He has published around 40 papers in refereed international journals. His research interests include nonlinear stochastic control and filtering, as well as multi-agent systems and sensor networks. Dr Ding is serving as an Associate Editor for Neurocomputing and IET Control Theory $ Application. He is also a very active reviewer for many international journals.

Hongjian Liu

Hongjian Liu received his BSc degree in applied mathematics in 2003 from Anhui University, Hefei, China and the MSc degree in detection technology and automation equipment in 2009 from Anhui Polytechnic University, Wuhu, China. He is currently pursuing the PhD degree in control science and engineering from Donghua University, Shanghai, China. He is also an Associate Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. Dr Liu’s current research interests include filtering theory, memristive neural networks and network communication systems. He is a very active reviewer for many international journals.

Xueli Wang

Xueli Wang received the BSc degree from Qufu Normal University, Qufu, China, in 2013. She is currently pursuing the PhD degree in Control Science and Engineering from University of Shanghai for Science and Technology, Shanghai, China. Her current research interests include networked control systems, adaptive dynamic program, and neural networks. She is a very active reviewer for many international journals.